In this section we investigate the statistical properties of the PCAN and sPCAN methods. We first describe the relationship between the two methods, and then describe the large sample (\(N \rightarrow \infty \) ) asymptotics of the principal components output by the sPCAN algorithm described in Section . Our analysis assumes that the observed sample of graphs are drawn from a family of kernel-based random graphs (KRGs). The family of KRGs is a widely studied class of random graph models that contain many popular statistical network models for unweighted graphs [1]}, including the Erdős-Rényi random graph model [2]}, the stochastic block model [3]}, [4]}, the latent space model [5]}, the beta model [6]}, [7]}, as well as the random dot-product graph model [8]}, [9]}.
